Geometric property of off resonance error robust composite pulse

Abstract

The precision of quantum operations is affected by unavoidable systematic errors. A composite pulse (CP), which has been well investigated in nuclear magnetic resonance (NMR), is a technique that suppresses the influence of systematic errors by replacing a single operation with a sequence of operations. In one-qubit operations, there are two typical systematic errors, Pulse Length Error (PLE) and Off Resonance Error (ORE). Recently, it was found that PLE robust CPs have a clear geometric property. In this study, we show that ORE robust CPs also have a simple geometric property, which is associated with trajectories on the Bloch sphere of the corresponding operations. We discuss the geometric property of ORE robust CPs using two examples.

Short Composite Quantum Gate Robust against Two Common Systematic Errors

“…This is related to an intuitive explanation of the detuning robustness introduced in Ref. [48]. For a detuning-robust control, its "mass center" of the trajectory in the Bloch sphere representation must lie on the xy plane.…”

“…This behavior is not the same as the case of θ f = π/2 even though the target operation for these cases are the same up to the global phase of the unitary matrix. The discord between both cases is intuitively explained by the aforementioned mass-center representation of the detuning robustness [48]: As the trajectory of the direct operation for θ f = 3π/2 has the mass center near the origin comparing with the case of θ f = π/2, a slight modification of the dynamics is sufficient to attain the robustness. As discussed later, the monotonicity of the pulse-area optimal control makes its pulse area be the same as that of the direct operation.…”